Spectral theory of operator pencils, HermiteBiehler functions, and their applications
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The work Spectral theory of operator pencils, HermiteBiehler functions, and their applications represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Spectral theory of operator pencils, HermiteBiehler functions, and their applications
Resource Information
The work Spectral theory of operator pencils, HermiteBiehler functions, and their applications represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Spectral theory of operator pencils, HermiteBiehler functions, and their applications
 Statement of responsibility
 Manfred Möller, Vyacheslav Pivovarchik
 Language
 eng
 Summary
 The theoretical part of this monograph examines the distribution of the spectrum of operator polynomials, focusing on quadratic operator polynomials with discrete spectra. The second part is devoted to applications. Standard spectral problems in Hilbert spaces are of the form AnI for an operator A, and selfadjoint operators are of particular interest and importance, both theoretically and in terms of applications. A characteristic feature of selfadjoint operators is that their spectra are real, and many spectral problems in theoretical physics and engineering can be described by using them. However, a large class of problems, in particular vibration problems with boundary conditions depending on the spectral parameter, are represented by operator polynomials that are quadratic in the eigenvalue parameter and whose coefficients are selfadjoint operators. The spectra of such operator polynomials are in general no more real, but still exhibit certain patterns. The distribution of these spectra is the main focus of the present volume. For some classes of quadratic operator polynomials, inverse problems are also considered. The connection between the spectra of such quadratic operator polynomials and generalized HermiteBiehler functions is discussed in detail. Many applications are thoroughly investigated, such as the Regge problem and damped vibrations of smooth strings, Stieltjes strings, beams, star graphs of strings and quantum graphs. Some chapters summarize advanced background material, which is supplemented with detailed proofs. With regard to the reader's background knowledge, only the basic properties of operators in Hilbert spaces and wellknown results from complex analysis are assumed
 Cataloging source
 N$T
 Dewey number
 515.7222
 Index
 index present
 LC call number
 QC20.7.S64
 LC item number
 M65 2015eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Operator theory: advances and applications
 Series volume
 v. 246
Context
Context of Spectral theory of operator pencils, HermiteBiehler functions, and their applicationsWork of
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